The emergence and re-emergence of viruses has highlighted the need to develop new broad-spectrum antivirals to mitigate human infections. Pursuing our search for new bioactive plant-derived molecules, we study several diterpene derivatives synthesized from jatropholones A and B and carnosic acid isolated from Jatropha isabellei and Rosmarinus officinalis, respectively. Here, we investigate the antiviral effect of the diterpenes against human adenovirus (HAdV-5) that causes several infections for which there is no approved antiviral therapy yet. Ten compounds are evaluated and none of them present cytotoxicity in A549 cells. Only compounds 2, 5 and 9 inhibit HAdV-5 replication in a concentration-dependent manner, without virucidal activity, whereas the antiviral action takes place after virus internalization. The expression of viral proteins E1A and Hexon is strongly inhibited by compounds 2 and 5 and, in a lesser degree, by compound 9. Since compounds 2, 5 and 9 prevent ERK activation, they might exert their antiviral action by interfering in the host cell functions required for virus replication. Besides, the compounds have an anti-inflammatory profile since they significantly inhibit the levels of IL-6 and IL-8 produced by THP-1 cells infected with HAdV-5 or with an adenoviral vector. In conclusion, diterpenes 2, 5 and 9 not only exert antiviral activity against adenovirus but also are able to restrain pro-inflammatory cytokines induced by the virus.